Page:Transactions NZ Institute Volume 16.djvu/33

Rh Dr. Halley, of comet renown, who died in 1742, left to his countrymen, not only the famous prediction of the return of his comet, which has since been twice verified at the appointed times, but also the most earnest recommendation to observe the transits of Venus of 1761 and 1769. Halley's injunction was well obeyed, especially in 1769, when the observations of Captain Cook's expedition at Otaheite, combined with observations at other stations in various parts of the world, resulted in the conclusion, until recently relied on as correct, that 95,000,000 miles is the true distance of the sun.

The mention of the honoured name of Cook recalls to mind how close the association is between the observation of the transit of Venus in 1769 and the rediscovery and settlement of these southern lands.

The principle of the observation is that followed by the surveyor in ascertaining the distance of an inaccessible object. A line is measured on the ground, also the two angles which it forms with the inaccessible point; the third angle of the triangle is then inferred, and the computation of the distance required is one of the simplest in plane trigonometry. But the distance to the inaccessible sun is so immeasurably great that any base line which the surveyor could mark off on the earth's surface would be as useless for the purpose as a mathematical point. Even if we could stay the sun in his course, and grant other impossible conditions, the most delicate instrument would fail to show any convergence of the sides of the wished-for triangle. In other words, there would be no parallax.

The solution of the problem must be tried in some other way, and the most obvious thing to do, in the first instance, is to increase the length of the base. The longest possible base on the earth is, oi course, the diameter of the earth itself. By placing observers suitably, in widely separated parts of the globe, the longest practicable base will be obtained, but still the problem is insoluble, unless we can have some intermediate body of known rate of circular motion coming in line between the observers and the sun. In the problem before us, Venus is that body, and, as she is, at transit, nearer the earth than the sun in the ratio of about 2 to 5, it will be seen that, to observers widely apart, Venus must necessarily come in line with the edge of the sun at different times to the two observers; just as would be the case were two observers, standing apart on the bank of a river, each to signal as a passing boat came in line with a tree on the opposite bank. It would be seen that an interval of time elapsed between the two signals. This interval, in the case of Venus, gives the measure of the angle subtended at the sun by the base line joining the stations of the observers. For the rate of the motion of Venus relative to that of the earth being known, the interval observed is convertible into